At the same time that photography was still primarily a B&W activity, others were researching and developing theories of human perception of color and models that could be used to describe the colors that humans perceive. Albert Munsell did exhaustive research in the decade between 1900 and 1910 and developed his color model which expresses color based on value (brightness, or tone), chroma (saturation), and hue (color).
The Munsell model is generally accepted today, although it is now understood that the shape of the limits of human color perception is not a tidy cylinder or sphere when expressed using the Munsell system. It looks more like this (with part of the area between blue and red cutaway to show the internal structure of the model.
Many of the terms listed in the question, however, have been around much longer than Munsell's system. Some of them originated in different languages than others and they sometimes have overlapping but slightly different shades of meaning. (See what I did there?)
Some of these terms mean one thing to a classically trained painter, and another to a photographer trained during the B&W era. What follows is how the terms are used in photography.
Hue - The angular position on the color wheel illustrated above. Green or Green-Yellow or Yellow or Yellow Red or Red, etc.
Chroma - The distance from the neutral center in the Mansell model. Near the center the hue is very muted. At the edges it is very intense, but it is the same hue.
Saturation - The combination of chroma and value. Hues look more "colorful" when they are near the middle of the value axis. If they are very dark, they don't look much different from black, if they are very bright they don't look much different from white. But a color with a high chroma and a value near five is very "colorful" a/k/a "saturated." With the RGB color model 'saturation' also means one or more of the three color channels is at 100% or full value. That channel can be said to be fully saturated.
Value - How white or black a shade of gray is. In color theory white and black are different brightness level of the same absence of hue. That is, no color is present.
Tone - In B&W photography it is strictly the same thing as value. In color photography it is also properly understood to mean 'value' when used alone. "Color tone", however can be used to refer to the total combination of color (chroma + hue) and value (brightness).
Tint - A word left over from the days before photography, it refers to what a painter would add to a color pigment to make it more white or more black. In the RGB color model 'tint' refers to the green←→magenta axis that is roughly perpendicular to the blue←→amber 'color temperature' axis.
Shade - Another leftover from painting that describes the darkening half of 'tint'. "Shading" a paint meant adding black to a color pigment to make it darker and thus have a lower tonal value.
Intensity - Mostly synonymous with value, but can sometimes also be used to denote a high degree of chroma. "Those flowers were such an intense shade of yellow that I thought they were going to blind me!"
Brightness - Similar to 'intensity', but less likely to be used to denote chroma instead of value.
Lightness - the other end from "shade' on the 'tint' scale with regard to adding white powder to a pigment to make it lighter. In photography it also refers to a higher number on the 'value' scale..